Page 53 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 3 Sistem Persamaan
4. Nyatakan jenis penyelesaian bagi setiap sistem persamaan linear berikut. SP 3.1.2 TP2
State the type of solution of each of the following systems of linear equations.

(i) 2x + y + 3z = 5 ................. (ii) 2x + 2y + z = 18 .................
−3x + y + z = 8 .................b 3x − 4y + z = 10 .................b
−4x − 2y − 6z = 2 ............c 5x − 2y + 2z = 28 ...............c
b − : −5x − 2z = 3 ...................d b − : x − 6y = −8 .............d
b × 2: −6x + 2y + 2z = 16 ..........e b × 2: 6x − 8y + 2z = 20 ..........e
c + e: −10x − 4z = 18 ..............f e − c x − 6y = −8 ..............f
d × 2: −10x − 4z = 6 ...................g d − f: 0 = 0
f – g: 0 = 12 Maka, sistem persamaan linear ini mempunyai
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Maka, sistem persamaan linear ini tidak penyelesaian tak terhingga.
mempunyai penyelesaian. Thus, this system of linear equations has infinite solutions.
Thus, this system of linear equations has no solution.

(a) x + 2y + 3z = 16 ...................... (b) −2x + y + 3z = 5 ......................
2x + 3y + 2z = 78 ....................b 2x + y + z = 2 ...........................b
4x + 7y + 8z = 202 .................c 2x + 3y + 5z = 9 ......................c

 × 2: 2x + 4y + 6z = 32 .................d  + b: 2y + 4z = 7 ......................d
d − b: y + 4z = −46 ..........................e c − b: 2y + 4z = 7 ......................e
d − e: 0 = 0
b × 2: 4x + 6y + 4z = 156 .................f
c − f: y + 4z = 46 .............................g Maka, sistem persamaan linear ini mempunyai
e − g: 0 = −92 penyelesaian tak terhingga.
Thus, this system of linear equations has infinite solutions.
Maka, sistem persamaan linear ini tidak
mempunyai penyelesaian.
Thus, this system of linear equations has no solution.

5. Selesaikan setiap yang berikut. SP 3.1.3
Solve each of the following.
(a) Kedai Kek Lilycious membuat tiga jenis kek, P, Q dan R, yang menggunakan tiga jenis bahan mentah
iaitu mentega, gula dan tepung. Jadual di bawah menunjukkan jisim mentega, gula dan tepung untuk
membuat sebiji kek. TP4
Kedai Kek Lilycious makes three types of cakes, P, Q and R, which use three types of raw materials that are butter, sugar and flour. The
table below shows the weights of butter, sugar and flour to make a cake.
Kek P Kek Q Kek R
Cake P Cake Q Cake R
Mentega
Butter 0.2 kg 0.4 kg 0.3 kg
Gula 0.3 kg 0.4 kg 0.4 kg
Sugar
Tepung 0.5 kg 0.2 kg 0.3 kg
Flour

Bekalan mentega, gula dan tepung yang boleh digunakan untuk membuat kek-kek tersebut masing-
masing ialah 30 kg, 40 kg dan 35 kg. Cari bilangan kek bagi setiap jenis kek yang boleh dibuat oleh
Kedai Kek Lilycious.
The supply of butter, sugar and flour can be used to make the cakes are 30 kg, 40 kg and 35 kg respectively. Find the number of cakes
of each type of cake that can be made by Kedai Kek Lilycious.

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